Meta: there are several existing Qs for single-member LLC, but I can't find a dupe for multi-member.
For US tax an LLC is by default disregarded as passthrough if single member, or treated as partnership if multi member, which is your case, and yes partnership files 1065 with K-1's for each partner (which must add to 100%, so 33x3 is not quite enough). Partnership profits don't have to be actually distributed, but both income and expenses must be allocated, and the partners report and pay individual tax on the amounts allocated whether or not actually distributed. Basically, in law the assets of the partnership are owned by the partners, so you have already 'have' the profit even if you didn't take individual possession.
A few LLCs must, and others (likely including yours) may elect to, be treated for tax purposes as a corporation, and file 1120, with 1099-DIV for any payouts. In that case the corporation as an entity pays tax on its profits, whether retained for future use or paid out to the shareholders. In that case you were supposed to be making almost-quarterly estimated payments during the year and may owe a penalty for failing to do so. Individuals in general are similarly supposed to make estimated payments if you have taxable income without withholding, but at $10k/3 each, even with SE tax, you are likely under or at least fairly near the penalty threshold = 10% of tax liability or $1k whichever is more -- and if this is a 'side' job for you and your partners, i.e. you also have job income with withholding, there is a safe-harbor if your withholding was sufficient to pay 100% (110% over $150k AGI) of the prior year tax. I don't know if any similar escape is available for a newly-filing corporation.
Note the filing deadline for partnerships is March 15 -- this week. This is designed to allow at least a little time for partners to receive their K-1's and still prepare their individual returns by April 15. But you can request on extension on form 7004, including online -- see IRS website).